TORONTO -- It was a weak group effort for the Islanders in the first period Thursday night when they fell behind the Maple Leafs by two goals and were badly outplayed.

But starting in the second period, a strong group effort rallied them to five straight goals and a 7-4 win. It was the sort of composed recovery that the Islanders have not been able to produce consistently.

"We obviously can't have those kinds of starts, because they'll hurt you more often than not," Andrew MacDonald said. "But going forward, it's another lesson learned. Our intensity level wasn't where it needed to be, we addressed it in the room and we played a smarter game."

They got scoring from all corners of the lineup. Matt Moulson had his first two goals of the season, Michael Grabner scored two in the third, including the game-winner, and Brad Boyes had a goal and two assists in his first impactful night as an Islander.

"Everyone chipped in, which is great to see," said John Tavares, who had two assists for the second straight game. "We needed to get back to what we do well, which is move our feet and get cycling down low in the offensive zone. All four lines got that going."

Tavares' line was the only one going in a sluggish first period. Moulson scored off a broken play to tie the score at 1-1, but the Leafs had all kinds of room to operate in the opening 20 minutes, outshooting the Isles 16-9 and producing a 3-1 lead that could have been larger if the Isles hadn't killed off 25 seconds of a two-man Leafs advantage at the end of the period.

"Our gaps were bad in our zone. We weren't making good dump-ins," Matt Carkner said. "What we did after that is how we've got to play, with everyone putting in the effort."

Mark Streit's power-play goal at 11:44 of the second, off a nice look from Boyes along the side wall, started things moving. Boyes redirected Frans Nielsen's feed just 1:26 later, the sort of big-effort play the Isles were talking about. Nielsen lost a Leafs zone draw, but he and Grabner outworked three Leafs to regain possession as Boyes cruised to the front of the net for the tip-in.

The Isles got a couple of gifts early in the third when Grabner's long-range wrist shot eluded Ben Scrivens and Keith Aucoin's quick shot beat Scrivens through the pads just 1:12 later.

The Leafs changed goaltenders and the game got a bit hairy in the closing minutes. Moulson made it 6-3, the Leafs cut it to 6-4 and Aucoin swept a puck off the goal line with just under two minutes to go before Grabner scored into an empty net to seal it.

Evgeni Nabokov let in four goals but still had 39 saves in a performance that got better as the night went on.

Jack Capuano saw progress during the final 40 minutes, but it's not a big accomplishment to him.

"We addressed it with this group early on in camp. We've got to expect to win," he said. "There are guys in this room who have been here long enough. They need to take ownership and be more vocal at times when we need it."